A Universal Relation Between Cosmological Expansion Tensions and Atomic Clock Stability

We propose Dynamical Temporal Relaxation (DTR), a covariant scalar-field framework in which the rate of proper time evolves relative to cosmological expansion via a conformal coupling of matter to a rescaled metric. The model resolves the Hubble (H₀) and σ₈ tensions while remaining consistent with early-universe constraints (z ~ 1100), where the field is dynamically suppressed. A key prediction is a universal common-mode fractional frequency drift in atomic clock ensembles at the level of ~10⁻¹⁸ yr⁻¹. This signal appears in ensemble averages while canceling in differential comparisons and is testable using existing datasets (e.g., BIPM Circular T). This version includes references connecting the framework to ΛCDM, scalar–tensor theories, and precision metrology.